Gravitational Forces and Fields Quiz

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Questions and Answers

What is the dimension of the gravitational constant G?

  • [M^1L^2T^0]
  • [M^1L^1T^{-1}]
  • [M^0L^1T^1]
  • [M^{-1}L^3T^{-2}] (correct)

What happens to the value of gravitational field intensity (g) as one goes deeper into the Earth?

  • It remains constant regardless of depth.
  • It varies inversely with depth.
  • It decreases linearly with depth. (correct)
  • It increases linearly with depth.

Which of the following is a characteristic of gravitational force?

  • It can be repulsive.
  • It only affects massive bodies.
  • It requires other bodies to exert a force.
  • It is a mutual force between all bodies. (correct)

When calculating the weight of an object, which formula is used?

<p>$w = mg$ (B)</p> Signup and view all the answers

If the distance from the center of the Earth is doubled, how does gravitational force change according to the formula $F = G rac{m_1 m_2}{r^2}$?

<p>It decreases to a quarter of the original force. (B)</p> Signup and view all the answers

What is the relationship between gravitational force and the distance between two masses according to Newton's Law of Universal Gravitation?

<p>It is inversely proportional to the distance squared. (C)</p> Signup and view all the answers

In a uniform spherical shell, what happens to the gravitational field inside the shell?

<p>It is zero. (B)</p> Signup and view all the answers

What is the SI unit of gravitational potential?

<p>J/kg (C)</p> Signup and view all the answers

How does the gravitational potential due to a point mass behave?

<p>It is always negative. (D)</p> Signup and view all the answers

What type of field is produced by a uniformly distributed mass when observed from an external point?

<p>Attractive and conservative. (A)</p> Signup and view all the answers

What is the expression for the gravitational potential at a point outside a uniform solid sphere?

<p>$V(r) = - rac{GM}{r}$ (B)</p> Signup and view all the answers

Which of the following gives the gravitational potential at the center of a uniform solid sphere?

<p>$V = - rac{3GM}{2R}$ (C)</p> Signup and view all the answers

How does the gravitational potential change with distance for points inside a uniform solid sphere?

<p>It decreases quadratically with distance. (A)</p> Signup and view all the answers

What is the relationship between the change in gravitational potential and the gravitational field strength?

<p>$dV = -E imes dr$ (C)</p> Signup and view all the answers

How would you describe the graph of gravitational potential versus distance for external points relative to the uniform solid sphere?

<p>It resembles a hyperbola. (D)</p> Signup and view all the answers

Flashcards

Gravitational Force Formula

The force of attraction between two objects with mass is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Gravitational Constant

A universal physical constant (G) used in the law of universal gravitation.

Universal Gravitation

Gravity affects everything with mass, everywhere in space.

Mutual Gravitational Force

Every object attracts every other object with a force.

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Attractive Gravitational Force

The force of gravity always pulls objects together never pushes them apart.

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Gravitational Field Intensity

The force per unit mass experienced by an object in a gravitational field.

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Variation of g with Height

Gravitational acceleration (g) decreases with increasing height above Earth`s surface.

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Variation of g with Depth

Gravitational acceleration (g) decreases with increasing depth below Earth`s surface.

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Gravitational Field Intensity Formula

The strength of a gravitational field at a point is determined by the mass and distance of the source object.

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Weight Formula

Weight is the product of mass and gravitational acceleration.

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Calculation of g on Earth's surface

The acceleration due to gravity on Earth's surface depends on Earth's mass and radius.

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Newton's Law of Universal Gravitation

Describes the attractive force between any two masses in the universe.

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Gravitational Constant (G)

A constant of proportionality in Newton's law of universal gravitation.

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Gravitational Field (Uniform)

Field due to a uniform sphere at an external point; field strength is proportional to the mass, inversely proportional to the square of the distance from the mass center.

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Gravitational Field (Uniform Spherical Shell - external point)

At an external point from the spherical shell, the field is equivalent to a point mass at the center.

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Gravitational Field (Uniform Spherical Shell - internal point)

Zero.

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Gravitational Potential

Scalar quantity that describes the amount of work needed to move a unit mass from infinity to a given point in space in a gravitational field.

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Gravitational Potential (SI unit)

Joules/kilogram (J/kg)

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Gravitational Potential (Properties)

Scalar, negative for point masses, and independent of the path.

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Gravitational Force (Nature)

Always attractive

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Gravitational Field (Conservative)

Work done by gravitational force does not depend on path.

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Potential at External Point

The gravitational potential at a point outside a uniform solid sphere, given by the formula V(r) = -GM/r, where r is the distance from the sphere's center.

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Potential at Internal Point

The gravitational potential at a point inside a uniform solid sphere, given by the formula V(r) = -GM/R(1 - r^2/3R^2).

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Gravitational Potential

Energy per unit mass associated with a gravitational field.

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Gravitational Field

Region around a mass where any other mass experiences a force.

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Potential vs. Distance (External)

Potential decreases as distance increases, following a hyperbola graph.

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Potential vs. Distance (Internal)

Potential decreases at a parabolic rate; varies differently inside as distance changes.

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Relation between Potential and Field

The change in potential (dV) equals the negative of the field (E) multiplied by the change in distance (dr).

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Gravitational Constant (G)

A constant that appears in the equations for gravity.

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